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Simplifying ((x2) + -1(2x) + -1(100000)) = 0 (x2 + -1(2x) + -1(100000)) = 0 Remove parenthesis around (2x) (x2 + -1 * 2x + -1(100000)) = 0 Multiply -1 * 2 (x2 + -2x + -1(100000)) = 0 Multiply -1 * 100000 (x2 + -2x + -100000) = 0 Reorder the terms: (-100000 + -2x + x2) = 0 Remove parenthesis around (-100000 + -2x + x2) -100000 + -2x + x2 = 0 Solving -100000 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100000' to each side of the equation. -100000 + -2x + 100000 + x2 = 0 + 100000 Reorder the terms: -100000 + 100000 + -2x + x2 = 0 + 100000 Combine like terms: -100000 + 100000 = 0 0 + -2x + x2 = 0 + 100000 -2x + x2 = 0 + 100000 Combine like terms: 0 + 100000 = 100000 -2x + x2 = 100000 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 100000 + 1 Reorder the terms: 1 + -2x + x2 = 100000 + 1 Combine like terms: 100000 + 1 = 100001 1 + -2x + x2 = 100001 Factor a perfect square on the left side: (x + -1)(x + -1) = 100001 Calculate the square root of the right side: 316.229347152 Break this problem into two subproblems by setting (x + -1) equal to 316.229347152 and -316.229347152.Subproblem 1
x + -1 = 316.229347152 Simplifying x + -1 = 316.229347152 Reorder the terms: -1 + x = 316.229347152 Solving -1 + x = 316.229347152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 316.229347152 + 1 Combine like terms: -1 + 1 = 0 0 + x = 316.229347152 + 1 x = 316.229347152 + 1 Combine like terms: 316.229347152 + 1 = 317.229347152 x = 317.229347152 Simplifying x = 317.229347152Subproblem 2
x + -1 = -316.229347152 Simplifying x + -1 = -316.229347152 Reorder the terms: -1 + x = -316.229347152 Solving -1 + x = -316.229347152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -316.229347152 + 1 Combine like terms: -1 + 1 = 0 0 + x = -316.229347152 + 1 x = -316.229347152 + 1 Combine like terms: -316.229347152 + 1 = -315.229347152 x = -315.229347152 Simplifying x = -315.229347152Solution
The solution to the problem is based on the solutions from the subproblems. x = {317.229347152, -315.229347152}
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